The rectangular plate shown weighs 75 lb and is held in the position shown by hinges at A and B and by cable EF. Assuming that the hinge at B does not exert any axial thrust, determine (a) the tension in the cable, (b) the reactions at A and B.
(a)
The tension in the cable.
Answer to Problem 4.152RP
The tension in the cable is
Explanation of Solution
The free-body diagram is shown in figure 1.
Write the expression for the tension in the cable.
Here,
Write the expression of the vector
Find the magnitude of the vector
Put equations (II) and (III) in equation (I).
Write the expressions for the position vectors.
Here,
Sum of the moments of the forces about the point A must be zero.
Here,
Write the expression for the sum of the moments about the point A.
Here,
Put the above equation in equation (VI) and use determinants.
Conclusion:
Equate the coefficient of
Thus, the tension in the cable is
(b)
The reactions at A and B.
Answer to Problem 4.152RP
The reaction at A is
Explanation of Solution
Equate the coefficient of
Here,
Substitute
Equate the coefficient of
Here,
Substitute
Write the expression for
Substitute
Refer figure 1.
The net force must be equal to zero.
Here,
Write the expression for the net force.
Here,
Put the above equation in equation (VIII).
Equate the coefficient of
Equate the coefficient of
Equate the coefficient of
Write the expression of
Conclusion:
Thus, the reaction at A is
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Chapter 4 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics
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